at of uniformly accelerated motion, under the action of a constant
force, similar to that which is presented by falling bodies;[1] and
finally,

6th. How to find the coefficient, by which the amount of centrifugal
force exerted in any case may be computed.

[Footnote 1: A body revolving with a uniform velocity in a horizontal
plane would present the only case of uniformly accelerated motion that
is possible to be realized under actual conditions.]

I now pass to some other features.

_First_.--You will observe that, relatively to the center, a revolving
body, at any point in its revolution, is at rest. That is, it has no
motion, either from or toward the center, except that which is produced
by the action of the centripetal force. It has, therefore, this identity
also with a falling body, that it starts from a state of rest. This
brings us to a far more comprehensive definition of centrifugal force.
This is the resistance which a body opposes to being put in motion, at
any velocity acquired in any time, from a state of rest. Thus
centrifugal force reveals to us the measure of the inertia of matter.
This inertia may be demonstrated and exhibited by means of apparatus
constructed on this principle quite as accurately as it can be in any
other way.

_Second_.--You will also observe the fact, that motion must be imparted
to a body gradually. As distance, _through_ which force can act, is
necessary to the impartation of velocity, so also time, _during_ which
force can act, is necessary to the same result. We do not know how
motion from a state of rest begins, any more than we know how a polygon
becomes a circle. But we do know that infinite force cannot impart
absolutely instantaneous motion to even the smallest body, or to a body
capable of opposing the least resistance. Time being an essential
element or factor in the impartation of velocity, if this factor be
omitted, the least resistance becomes infinite.

We have a practical illustration of this truth in the explosion of
nitro-glycerine. If a small portion of this compound be exploded on the
surface of a granite bowlder, in the open air, the bowlder will be rent
into fragments. The explanation of this phenomenon common among the
laborers who are the most numerous witnesses of it, which you have
doubtless often heard, and which is accepted by ignorant minds without
further thought, is that the action of nitro-glycerine is downward. We
know that such an idea is abs